But the admirals suggest the scale of the commitment could mean that the UK government would have to "obtain our European partners' approval if we wished to use them on a purely national issue".
Prominent on the agenda at the one-day summit were the US plans for a national missile defence shield and European proposals for a rapid reaction force.
Mr Bush said that the missile defence system was a necessary step "to enhance freedom" in the face of new threats from rogue states or groups.
Opposition to stance
Mr Blair said: "The most important thing is that Europe and America should always stick together.
"Of course there will be areas where we need intensive negotiations, like nuclear defence, but the world is a more secure and more stable place if Europe and America are together."
But Mr Blair's comments did not go far enough in support of the US plan, according to shadow defence secretary Iain Duncan Smith.
He said: "If we do not give the Americans support the plan will go ahead anyway, but without our having any influence over it.
"Britain and Europe are as vulnerable to threats from rogue states as the US... it is vital that Tony Blair shows some real leadership in backing George W Bush on missile defence."
European Army row
Mr Blair was warned by two senior admirals earlier on Wednesday that the Rapid Reaction Force could undermine relations between the UK and the USA.
Admiral Sir John Woodward and vice-admiral Sir John Roxburgh wrote a letter to the Daily Telegraph suggesting the UK was committing too much infantry to the proposed force - due to be operational by 2003.
The government has pledged to contribute 12,500 ground troops to the 60,000 strong force, 18 warships and 72 combat aircraft.
But the admirals suggest the scale of the commitment could mean that the UK government would have to "obtain our European partners' approval if we wished to use them on a purely national issue".
They add: "We believe it is far preferable to have a full and proper debate on the Euro force rather than risk undermining our rare and immensely valuable relationship with the Americans in exchange for an essentially political gesture towards a federal Europe."
Fears dismissed
Replying to the letter, Defence Secretary Geoff Hoon said: "There is no plan for a 'common Euro army'.
"Our approach to European defence envisages nothing of the sort.
"Decisions on committing forces to a European-led military operation will be taken in national capitals in the same way as happens for Nato.
"No one talks about a 'common Euro army'."